The Internet Corporation for Assigned Names and Numbers (ICANN) is a nonprofit organization responsible for coordinating the Internet's naming system, and making sure that the network has a stable and secure operation. Unfortunately, when you buy or register a domain from us, we are obliged to add the registrant (or your) details to the WHOIS database. This is a requirement from ICANN, the organisation who manages all Generic Top-level domains (gTLDs).
Yes, it is possible for some domains. For example, for most generic top-level domains you can buy and activate ID Protection (Domain Privacy).